Peering into the crystal ball: Excess entropy scaling predicts equilibrium transport coefficients before equilibration

Abstract

In a molecular-dynamics simulation, an equilibrium transport coefficient is to be computed (as the name suggests) in a system that has reached thermodynamic equilibrium. Indeed, the two most common methods for computing equilibrium transport coefficients—using the Einstein–Helfand (EH) relation and using the Green–Kubo (GK) relation—make the formal assumption that a system has reached thermodynamic equilibrium before sampling begins. There is, however, “no free lunch”: Equilibration always demands an upfront computational investment. In this work, we study the question of just how much equilibration is needed for each computational method to yield a serviceable estimate for a transport coefficient, using as our case study a simple fluid that is initialized far out of configurational equilibrium. We show that a third method for computing transport coefficients—excess entropy scaling, which makes use of system structure in the form of the radial distribution function—has several statistically beneficial properties as compared to EH and GK, including faster convergence to the long-time-average value of the transport coefficient and lower sample-to-sample variance en route to convergence, which we rationalize from an information-theoretic perspective. Overall, this work points to the significant value that structure-based estimators may bring to any workflow demanding high-throughput calculation of transport coefficients.